Hausdorff distance between two compact sets, defined as the maximum distance from a point of one set to another set, has many application in computer science. It is a good measure for the similarity of two sets. This ...Hausdorff distance between two compact sets, defined as the maximum distance from a point of one set to another set, has many application in computer science. It is a good measure for the similarity of two sets. This paper proves that the shape distance between two compact sets in R^n defined by nfinimum Hausdorff distance under rigid motions is a distance. The authors introduce similarity comparison problems in protein science, and propose that this measure may have good application to comparison of protein structure as well. For calculation of this distance, the authors give one dimensional formulas for problems （2, n）, （3, 3）, and （3, 4）. These formulas can reduce time needed for solving these problems. The authors did some data, this formula can reduce time needed to one As n increases, it would save more time. numerical experiments for （2, n）. On these sets of fifteenth of the best algorithms known on average.展开更多
基金supported by the National Natural Science Foundation of China under Grant No. 10771206973 Project (2004CB318000) of China
文摘Hausdorff distance between two compact sets, defined as the maximum distance from a point of one set to another set, has many application in computer science. It is a good measure for the similarity of two sets. This paper proves that the shape distance between two compact sets in R^n defined by nfinimum Hausdorff distance under rigid motions is a distance. The authors introduce similarity comparison problems in protein science, and propose that this measure may have good application to comparison of protein structure as well. For calculation of this distance, the authors give one dimensional formulas for problems （2, n）, （3, 3）, and （3, 4）. These formulas can reduce time needed for solving these problems. The authors did some data, this formula can reduce time needed to one As n increases, it would save more time. numerical experiments for （2, n）. On these sets of fifteenth of the best algorithms known on average.
